
(/VERSIONCHECK 2) 

(DEFUN |PGE;llli2gp| (|l| $)
  (SPADCALL (SPADCALL (ELT $ 8) |l| (QREFELT $ 13)) (QREFELT $ 15))) 

(DEFUN |PGE;li1n| (|n| $)
  (PROG (|i| #1=#:G1822)
    (RETURN
     (SEQ
      (PROGN
       (LETT #1# NIL . #2=(|PGE;li1n|))
       (SEQ (LETT |i| 1 . #2#) G190 (COND ((QSGREATERP |i| |n|) (GO G191)))
            (SEQ (EXIT (LETT #1# (CONS |i| #1#) . #2#)))
            (LETT |i| (QSADD1 |i|) . #2#) (GO G190) G191
            (EXIT (NREVERSE #1#)))))))) 

(DEFUN |PGE;youngGroup;LPg;3| (|l| $)
  (PROG (|element| |gens| #1=#:G1835 |i| #2=#:G1834 #3=#:G1833 |n|)
    (RETURN
     (SEQ (LETT |gens| NIL . #4=(|PGE;youngGroup;LPg;3|))
          (LETT |element| 1 . #4#)
          (SEQ (LETT |n| NIL . #4#) (LETT #3# |l| . #4#) G190
               (COND
                ((OR (ATOM #3#) (PROGN (LETT |n| (CAR #3#) . #4#) NIL))
                 (GO G191)))
               (SEQ
                (EXIT
                 (COND
                  ((SPADCALL |n| 1 (QREFELT $ 19))
                   (SEQ
                    (LETT |gens|
                          (CONS
                           (SPADCALL
                            (PROGN
                             (LETT #2# NIL . #4#)
                             (SEQ (LETT |i| |element| . #4#)
                                  (LETT #1# (- (+ |element| |n|) 1) . #4#) G190
                                  (COND ((> |i| #1#) (GO G191)))
                                  (SEQ (EXIT (LETT #2# (CONS |i| #2#) . #4#)))
                                  (LETT |i| (+ |i| 1) . #4#) (GO G190) G191
                                  (EXIT (NREVERSE #2#))))
                            (QREFELT $ 21))
                           |gens|)
                          . #4#)
                    (COND
                     ((>= |n| 3)
                      (LETT |gens|
                            (CONS (LIST (LIST |element| (+ |element| 1)))
                                  |gens|)
                            . #4#)))
                    (EXIT (LETT |element| (+ |element| |n|) . #4#)))))))
               (LETT #3# (CDR #3#) . #4#) (GO G190) G191 (EXIT NIL))
          (EXIT
           (|PGE;llli2gp|
            (COND ((EQL (LENGTH |gens|) 0) (LIST (LIST (LIST 1)))) ('T |gens|))
            $)))))) 

(DEFUN |PGE;youngGroup;PPg;4| (|lambda| $)
  (SPADCALL (SPADCALL |lambda| (QREFELT $ 24)) (QREFELT $ 22))) 

(DEFUN |PGE;rubiksGroup;Pg;5| ($)
  (PROG (|b| |l| |d| |u| |r| |f|)
    (RETURN
     (SEQ
      (LETT |f|
            (LIST (LIST 11 13 15 17) (LIST 12 14 16 18) (LIST 51 31 21 41)
                  (LIST 53 33 23 43) (LIST 52 32 22 42))
            . #1=(|PGE;rubiksGroup;Pg;5|))
      (LETT |r|
            (LIST (LIST 21 23 25 27) (LIST 22 24 26 28) (LIST 13 37 67 43)
                  (LIST 15 31 61 45) (LIST 14 38 68 44))
            . #1#)
      (LETT |u|
            (LIST (LIST 31 33 35 37) (LIST 32 34 36 38) (LIST 13 51 63 25)
                  (LIST 11 57 61 23) (LIST 12 58 62 24))
            . #1#)
      (LETT |d|
            (LIST (LIST 41 43 45 47) (LIST 42 44 46 48) (LIST 17 21 67 55)
                  (LIST 15 27 65 53) (LIST 16 28 66 54))
            . #1#)
      (LETT |l|
            (LIST (LIST 51 53 55 57) (LIST 52 54 56 58) (LIST 11 41 65 35)
                  (LIST 17 47 63 33) (LIST 18 48 64 34))
            . #1#)
      (LETT |b|
            (LIST (LIST 61 63 65 67) (LIST 62 64 66 68) (LIST 45 25 35 55)
                  (LIST 47 27 37 57) (LIST 46 26 36 56))
            . #1#)
      (EXIT (|PGE;llli2gp| (LIST |f| |r| |u| |d| |l| |b|) $)))))) 

(DEFUN |PGE;mathieu11;LPg;6| (|l| $)
  (PROG (|a|)
    (RETURN
     (SEQ (LETT |l| (SPADCALL |l| (QREFELT $ 27)) . #1=(|PGE;mathieu11;LPg;6|))
          (EXIT
           (COND
            ((SPADCALL (LENGTH |l|) 11 (QREFELT $ 28))
             (|error| "Exactly 11 integers for mathieu11 needed !"))
            ('T
             (SEQ
              (LETT |a|
                    (LIST
                     (LIST (SPADCALL |l| 1 (QREFELT $ 29))
                           (SPADCALL |l| 10 (QREFELT $ 29)))
                     (LIST (SPADCALL |l| 2 (QREFELT $ 29))
                           (SPADCALL |l| 8 (QREFELT $ 29)))
                     (LIST (SPADCALL |l| 3 (QREFELT $ 29))
                           (SPADCALL |l| 11 (QREFELT $ 29)))
                     (LIST (SPADCALL |l| 5 (QREFELT $ 29))
                           (SPADCALL |l| 7 (QREFELT $ 29))))
                    . #1#)
              (EXIT
               (|PGE;llli2gp|
                (LIST |a|
                      (LIST
                       (LIST (SPADCALL |l| 1 (QREFELT $ 29))
                             (SPADCALL |l| 4 (QREFELT $ 29))
                             (SPADCALL |l| 7 (QREFELT $ 29))
                             (SPADCALL |l| 6 (QREFELT $ 29)))
                       (LIST (SPADCALL |l| 2 (QREFELT $ 29))
                             (SPADCALL |l| 11 (QREFELT $ 29))
                             (SPADCALL |l| 10 (QREFELT $ 29))
                             (SPADCALL |l| 9 (QREFELT $ 29)))))
                $)))))))))) 

(DEFUN |PGE;mathieu11;Pg;7| ($) (SPADCALL (|PGE;li1n| 11 $) (QREFELT $ 30))) 

(DEFUN |PGE;mathieu12;LPg;8| (|l| $)
  (PROG (|a|)
    (RETURN
     (SEQ (LETT |l| (SPADCALL |l| (QREFELT $ 27)) . #1=(|PGE;mathieu12;LPg;8|))
          (EXIT
           (COND
            ((SPADCALL (LENGTH |l|) 12 (QREFELT $ 28))
             (|error| "Exactly 12 integers for mathieu12 needed !"))
            ('T
             (SEQ
              (LETT |a|
                    (LIST
                     (LIST (SPADCALL |l| 1 (QREFELT $ 29))
                           (SPADCALL |l| 2 (QREFELT $ 29))
                           (SPADCALL |l| 3 (QREFELT $ 29))
                           (SPADCALL |l| 4 (QREFELT $ 29))
                           (SPADCALL |l| 5 (QREFELT $ 29))
                           (SPADCALL |l| 6 (QREFELT $ 29))
                           (SPADCALL |l| 7 (QREFELT $ 29))
                           (SPADCALL |l| 8 (QREFELT $ 29))
                           (SPADCALL |l| 9 (QREFELT $ 29))
                           (SPADCALL |l| 10 (QREFELT $ 29))
                           (SPADCALL |l| 11 (QREFELT $ 29))))
                    . #1#)
              (EXIT
               (|PGE;llli2gp|
                (LIST |a|
                      (LIST
                       (LIST (SPADCALL |l| 1 (QREFELT $ 29))
                             (SPADCALL |l| 6 (QREFELT $ 29))
                             (SPADCALL |l| 5 (QREFELT $ 29))
                             (SPADCALL |l| 8 (QREFELT $ 29))
                             (SPADCALL |l| 3 (QREFELT $ 29))
                             (SPADCALL |l| 7 (QREFELT $ 29))
                             (SPADCALL |l| 4 (QREFELT $ 29))
                             (SPADCALL |l| 2 (QREFELT $ 29))
                             (SPADCALL |l| 9 (QREFELT $ 29))
                             (SPADCALL |l| 10 (QREFELT $ 29)))
                       (LIST (SPADCALL |l| 11 (QREFELT $ 29))
                             (SPADCALL |l| 12 (QREFELT $ 29)))))
                $)))))))))) 

(DEFUN |PGE;mathieu12;Pg;9| ($) (SPADCALL (|PGE;li1n| 12 $) (QREFELT $ 32))) 

(DEFUN |PGE;mathieu22;LPg;10| (|l| $)
  (PROG (|b| |a|)
    (RETURN
     (SEQ
      (LETT |l| (SPADCALL |l| (QREFELT $ 27)) . #1=(|PGE;mathieu22;LPg;10|))
      (EXIT
       (COND
        ((SPADCALL (LENGTH |l|) 22 (QREFELT $ 28))
         (|error| "Exactly 22 integers for mathieu22 needed !"))
        ('T
         (SEQ
          (LETT |a|
                (LIST
                 (LIST (SPADCALL |l| 1 (QREFELT $ 29))
                       (SPADCALL |l| 2 (QREFELT $ 29))
                       (SPADCALL |l| 4 (QREFELT $ 29))
                       (SPADCALL |l| 8 (QREFELT $ 29))
                       (SPADCALL |l| 16 (QREFELT $ 29))
                       (SPADCALL |l| 9 (QREFELT $ 29))
                       (SPADCALL |l| 18 (QREFELT $ 29))
                       (SPADCALL |l| 13 (QREFELT $ 29))
                       (SPADCALL |l| 3 (QREFELT $ 29))
                       (SPADCALL |l| 6 (QREFELT $ 29))
                       (SPADCALL |l| 12 (QREFELT $ 29)))
                 (LIST (SPADCALL |l| 5 (QREFELT $ 29))
                       (SPADCALL |l| 10 (QREFELT $ 29))
                       (SPADCALL |l| 20 (QREFELT $ 29))
                       (SPADCALL |l| 17 (QREFELT $ 29))
                       (SPADCALL |l| 11 (QREFELT $ 29))
                       (SPADCALL |l| 22 (QREFELT $ 29))
                       (SPADCALL |l| 21 (QREFELT $ 29))
                       (SPADCALL |l| 19 (QREFELT $ 29))
                       (SPADCALL |l| 15 (QREFELT $ 29))
                       (SPADCALL |l| 7 (QREFELT $ 29))
                       (SPADCALL |l| 14 (QREFELT $ 29))))
                . #1#)
          (LETT |b|
                (LIST
                 (LIST (SPADCALL |l| 1 (QREFELT $ 29))
                       (SPADCALL |l| 2 (QREFELT $ 29))
                       (SPADCALL |l| 6 (QREFELT $ 29))
                       (SPADCALL |l| 18 (QREFELT $ 29)))
                 (LIST (SPADCALL |l| 3 (QREFELT $ 29))
                       (SPADCALL |l| 15 (QREFELT $ 29)))
                 (LIST (SPADCALL |l| 5 (QREFELT $ 29))
                       (SPADCALL |l| 8 (QREFELT $ 29))
                       (SPADCALL |l| 21 (QREFELT $ 29))
                       (SPADCALL |l| 13 (QREFELT $ 29)))
                 (LIST (SPADCALL |l| 7 (QREFELT $ 29))
                       (SPADCALL |l| 9 (QREFELT $ 29))
                       (SPADCALL |l| 20 (QREFELT $ 29))
                       (SPADCALL |l| 12 (QREFELT $ 29)))
                 (LIST (SPADCALL |l| 10 (QREFELT $ 29))
                       (SPADCALL |l| 16 (QREFELT $ 29)))
                 (LIST (SPADCALL |l| 11 (QREFELT $ 29))
                       (SPADCALL |l| 19 (QREFELT $ 29))
                       (SPADCALL |l| 14 (QREFELT $ 29))
                       (SPADCALL |l| 22 (QREFELT $ 29))))
                . #1#)
          (EXIT (|PGE;llli2gp| (LIST |a| |b|) $)))))))))) 

(DEFUN |PGE;mathieu22;Pg;11| ($) (SPADCALL (|PGE;li1n| 22 $) (QREFELT $ 34))) 

(DEFUN |PGE;mathieu23;LPg;12| (|l| $)
  (PROG (|b| |a|)
    (RETURN
     (SEQ
      (LETT |l| (SPADCALL |l| (QREFELT $ 27)) . #1=(|PGE;mathieu23;LPg;12|))
      (EXIT
       (COND
        ((SPADCALL (LENGTH |l|) 23 (QREFELT $ 28))
         (|error| "Exactly 23 integers for mathieu23 needed !"))
        ('T
         (SEQ
          (LETT |a|
                (LIST
                 (LIST (SPADCALL |l| 1 (QREFELT $ 29))
                       (SPADCALL |l| 2 (QREFELT $ 29))
                       (SPADCALL |l| 3 (QREFELT $ 29))
                       (SPADCALL |l| 4 (QREFELT $ 29))
                       (SPADCALL |l| 5 (QREFELT $ 29))
                       (SPADCALL |l| 6 (QREFELT $ 29))
                       (SPADCALL |l| 7 (QREFELT $ 29))
                       (SPADCALL |l| 8 (QREFELT $ 29))
                       (SPADCALL |l| 9 (QREFELT $ 29))
                       (SPADCALL |l| 10 (QREFELT $ 29))
                       (SPADCALL |l| 11 (QREFELT $ 29))
                       (SPADCALL |l| 12 (QREFELT $ 29))
                       (SPADCALL |l| 13 (QREFELT $ 29))
                       (SPADCALL |l| 14 (QREFELT $ 29))
                       (SPADCALL |l| 15 (QREFELT $ 29))
                       (SPADCALL |l| 16 (QREFELT $ 29))
                       (SPADCALL |l| 17 (QREFELT $ 29))
                       (SPADCALL |l| 18 (QREFELT $ 29))
                       (SPADCALL |l| 19 (QREFELT $ 29))
                       (SPADCALL |l| 20 (QREFELT $ 29))
                       (SPADCALL |l| 21 (QREFELT $ 29))
                       (SPADCALL |l| 22 (QREFELT $ 29))
                       (SPADCALL |l| 23 (QREFELT $ 29))))
                . #1#)
          (LETT |b|
                (LIST
                 (LIST (SPADCALL |l| 2 (QREFELT $ 29))
                       (SPADCALL |l| 16 (QREFELT $ 29))
                       (SPADCALL |l| 9 (QREFELT $ 29))
                       (SPADCALL |l| 6 (QREFELT $ 29))
                       (SPADCALL |l| 8 (QREFELT $ 29)))
                 (LIST (SPADCALL |l| 3 (QREFELT $ 29))
                       (SPADCALL |l| 12 (QREFELT $ 29))
                       (SPADCALL |l| 13 (QREFELT $ 29))
                       (SPADCALL |l| 18 (QREFELT $ 29))
                       (SPADCALL |l| 4 (QREFELT $ 29)))
                 (LIST (SPADCALL |l| 7 (QREFELT $ 29))
                       (SPADCALL |l| 17 (QREFELT $ 29))
                       (SPADCALL |l| 10 (QREFELT $ 29))
                       (SPADCALL |l| 11 (QREFELT $ 29))
                       (SPADCALL |l| 22 (QREFELT $ 29)))
                 (LIST (SPADCALL |l| 14 (QREFELT $ 29))
                       (SPADCALL |l| 19 (QREFELT $ 29))
                       (SPADCALL |l| 21 (QREFELT $ 29))
                       (SPADCALL |l| 20 (QREFELT $ 29))
                       (SPADCALL |l| 15 (QREFELT $ 29))))
                . #1#)
          (EXIT (|PGE;llli2gp| (LIST |a| |b|) $)))))))))) 

(DEFUN |PGE;mathieu23;Pg;13| ($) (SPADCALL (|PGE;li1n| 23 $) (QREFELT $ 36))) 

(DEFUN |PGE;mathieu24;LPg;14| (|l| $)
  (PROG (|b| |a|)
    (RETURN
     (SEQ
      (LETT |l| (SPADCALL |l| (QREFELT $ 27)) . #1=(|PGE;mathieu24;LPg;14|))
      (EXIT
       (COND
        ((SPADCALL (LENGTH |l|) 24 (QREFELT $ 28))
         (|error| "Exactly 24 integers for mathieu24 needed !"))
        ('T
         (SEQ
          (LETT |a|
                (LIST
                 (LIST (SPADCALL |l| 1 (QREFELT $ 29))
                       (SPADCALL |l| 16 (QREFELT $ 29))
                       (SPADCALL |l| 10 (QREFELT $ 29))
                       (SPADCALL |l| 22 (QREFELT $ 29))
                       (SPADCALL |l| 24 (QREFELT $ 29)))
                 (LIST (SPADCALL |l| 2 (QREFELT $ 29))
                       (SPADCALL |l| 12 (QREFELT $ 29))
                       (SPADCALL |l| 18 (QREFELT $ 29))
                       (SPADCALL |l| 21 (QREFELT $ 29))
                       (SPADCALL |l| 7 (QREFELT $ 29)))
                 (LIST (SPADCALL |l| 4 (QREFELT $ 29))
                       (SPADCALL |l| 5 (QREFELT $ 29))
                       (SPADCALL |l| 8 (QREFELT $ 29))
                       (SPADCALL |l| 6 (QREFELT $ 29))
                       (SPADCALL |l| 17 (QREFELT $ 29)))
                 (LIST (SPADCALL |l| 9 (QREFELT $ 29))
                       (SPADCALL |l| 11 (QREFELT $ 29))
                       (SPADCALL |l| 13 (QREFELT $ 29))
                       (SPADCALL |l| 19 (QREFELT $ 29))
                       (SPADCALL |l| 15 (QREFELT $ 29))))
                . #1#)
          (LETT |b|
                (LIST
                 (LIST (SPADCALL |l| 1 (QREFELT $ 29))
                       (SPADCALL |l| 22 (QREFELT $ 29))
                       (SPADCALL |l| 13 (QREFELT $ 29))
                       (SPADCALL |l| 14 (QREFELT $ 29))
                       (SPADCALL |l| 6 (QREFELT $ 29))
                       (SPADCALL |l| 20 (QREFELT $ 29))
                       (SPADCALL |l| 3 (QREFELT $ 29))
                       (SPADCALL |l| 21 (QREFELT $ 29))
                       (SPADCALL |l| 8 (QREFELT $ 29))
                       (SPADCALL |l| 11 (QREFELT $ 29)))
                 (LIST (SPADCALL |l| 2 (QREFELT $ 29))
                       (SPADCALL |l| 10 (QREFELT $ 29)))
                 (LIST (SPADCALL |l| 4 (QREFELT $ 29))
                       (SPADCALL |l| 15 (QREFELT $ 29))
                       (SPADCALL |l| 18 (QREFELT $ 29))
                       (SPADCALL |l| 17 (QREFELT $ 29))
                       (SPADCALL |l| 16 (QREFELT $ 29))
                       (SPADCALL |l| 5 (QREFELT $ 29))
                       (SPADCALL |l| 9 (QREFELT $ 29))
                       (SPADCALL |l| 19 (QREFELT $ 29))
                       (SPADCALL |l| 12 (QREFELT $ 29))
                       (SPADCALL |l| 7 (QREFELT $ 29)))
                 (LIST (SPADCALL |l| 23 (QREFELT $ 29))
                       (SPADCALL |l| 24 (QREFELT $ 29))))
                . #1#)
          (EXIT (|PGE;llli2gp| (LIST |a| |b|) $)))))))))) 

(DEFUN |PGE;mathieu24;Pg;15| ($) (SPADCALL (|PGE;li1n| 24 $) (QREFELT $ 38))) 

(DEFUN |PGE;janko2;LPg;16| (|l| $)
  (PROG (|b| |a|)
    (RETURN
     (SEQ (LETT |l| (SPADCALL |l| (QREFELT $ 27)) . #1=(|PGE;janko2;LPg;16|))
          (EXIT
           (COND
            ((SPADCALL (LENGTH |l|) 100 (QREFELT $ 28))
             (|error| "Exactly 100 integers for janko2 needed !"))
            ('T
             (SEQ
              (LETT |a|
                    (LIST
                     (LIST (SPADCALL |l| 2 (QREFELT $ 29))
                           (SPADCALL |l| 3 (QREFELT $ 29))
                           (SPADCALL |l| 4 (QREFELT $ 29))
                           (SPADCALL |l| 5 (QREFELT $ 29))
                           (SPADCALL |l| 6 (QREFELT $ 29))
                           (SPADCALL |l| 7 (QREFELT $ 29))
                           (SPADCALL |l| 8 (QREFELT $ 29)))
                     (LIST (SPADCALL |l| 9 (QREFELT $ 29))
                           (SPADCALL |l| 10 (QREFELT $ 29))
                           (SPADCALL |l| 11 (QREFELT $ 29))
                           (SPADCALL |l| 12 (QREFELT $ 29))
                           (SPADCALL |l| 13 (QREFELT $ 29))
                           (SPADCALL |l| 14 (QREFELT $ 29))
                           (SPADCALL |l| 15 (QREFELT $ 29)))
                     (LIST (SPADCALL |l| 16 (QREFELT $ 29))
                           (SPADCALL |l| 17 (QREFELT $ 29))
                           (SPADCALL |l| 18 (QREFELT $ 29))
                           (SPADCALL |l| 19 (QREFELT $ 29))
                           (SPADCALL |l| 20 (QREFELT $ 29))
                           (SPADCALL |l| 21 (QREFELT $ 29))
                           (SPADCALL |l| 22 (QREFELT $ 29)))
                     (LIST (SPADCALL |l| 23 (QREFELT $ 29))
                           (SPADCALL |l| 24 (QREFELT $ 29))
                           (SPADCALL |l| 25 (QREFELT $ 29))
                           (SPADCALL |l| 26 (QREFELT $ 29))
                           (SPADCALL |l| 27 (QREFELT $ 29))
                           (SPADCALL |l| 28 (QREFELT $ 29))
                           (SPADCALL |l| 29 (QREFELT $ 29)))
                     (LIST (SPADCALL |l| 30 (QREFELT $ 29))
                           (SPADCALL |l| 31 (QREFELT $ 29))
                           (SPADCALL |l| 32 (QREFELT $ 29))
                           (SPADCALL |l| 33 (QREFELT $ 29))
                           (SPADCALL |l| 34 (QREFELT $ 29))
                           (SPADCALL |l| 35 (QREFELT $ 29))
                           (SPADCALL |l| 36 (QREFELT $ 29)))
                     (LIST (SPADCALL |l| 37 (QREFELT $ 29))
                           (SPADCALL |l| 38 (QREFELT $ 29))
                           (SPADCALL |l| 39 (QREFELT $ 29))
                           (SPADCALL |l| 40 (QREFELT $ 29))
                           (SPADCALL |l| 41 (QREFELT $ 29))
                           (SPADCALL |l| 42 (QREFELT $ 29))
                           (SPADCALL |l| 43 (QREFELT $ 29)))
                     (LIST (SPADCALL |l| 44 (QREFELT $ 29))
                           (SPADCALL |l| 45 (QREFELT $ 29))
                           (SPADCALL |l| 46 (QREFELT $ 29))
                           (SPADCALL |l| 47 (QREFELT $ 29))
                           (SPADCALL |l| 48 (QREFELT $ 29))
                           (SPADCALL |l| 49 (QREFELT $ 29))
                           (SPADCALL |l| 50 (QREFELT $ 29)))
                     (LIST (SPADCALL |l| 51 (QREFELT $ 29))
                           (SPADCALL |l| 52 (QREFELT $ 29))
                           (SPADCALL |l| 53 (QREFELT $ 29))
                           (SPADCALL |l| 54 (QREFELT $ 29))
                           (SPADCALL |l| 55 (QREFELT $ 29))
                           (SPADCALL |l| 56 (QREFELT $ 29))
                           (SPADCALL |l| 57 (QREFELT $ 29)))
                     (LIST (SPADCALL |l| 58 (QREFELT $ 29))
                           (SPADCALL |l| 59 (QREFELT $ 29))
                           (SPADCALL |l| 60 (QREFELT $ 29))
                           (SPADCALL |l| 61 (QREFELT $ 29))
                           (SPADCALL |l| 62 (QREFELT $ 29))
                           (SPADCALL |l| 63 (QREFELT $ 29))
                           (SPADCALL |l| 64 (QREFELT $ 29)))
                     (LIST (SPADCALL |l| 65 (QREFELT $ 29))
                           (SPADCALL |l| 66 (QREFELT $ 29))
                           (SPADCALL |l| 67 (QREFELT $ 29))
                           (SPADCALL |l| 68 (QREFELT $ 29))
                           (SPADCALL |l| 69 (QREFELT $ 29))
                           (SPADCALL |l| 70 (QREFELT $ 29))
                           (SPADCALL |l| 71 (QREFELT $ 29)))
                     (LIST (SPADCALL |l| 72 (QREFELT $ 29))
                           (SPADCALL |l| 73 (QREFELT $ 29))
                           (SPADCALL |l| 74 (QREFELT $ 29))
                           (SPADCALL |l| 75 (QREFELT $ 29))
                           (SPADCALL |l| 76 (QREFELT $ 29))
                           (SPADCALL |l| 77 (QREFELT $ 29))
                           (SPADCALL |l| 78 (QREFELT $ 29)))
                     (LIST (SPADCALL |l| 79 (QREFELT $ 29))
                           (SPADCALL |l| 80 (QREFELT $ 29))
                           (SPADCALL |l| 81 (QREFELT $ 29))
                           (SPADCALL |l| 82 (QREFELT $ 29))
                           (SPADCALL |l| 83 (QREFELT $ 29))
                           (SPADCALL |l| 84 (QREFELT $ 29))
                           (SPADCALL |l| 85 (QREFELT $ 29)))
                     (LIST (SPADCALL |l| 86 (QREFELT $ 29))
                           (SPADCALL |l| 87 (QREFELT $ 29))
                           (SPADCALL |l| 88 (QREFELT $ 29))
                           (SPADCALL |l| 89 (QREFELT $ 29))
                           (SPADCALL |l| 90 (QREFELT $ 29))
                           (SPADCALL |l| 91 (QREFELT $ 29))
                           (SPADCALL |l| 92 (QREFELT $ 29)))
                     (LIST (SPADCALL |l| 93 (QREFELT $ 29))
                           (SPADCALL |l| 94 (QREFELT $ 29))
                           (SPADCALL |l| 95 (QREFELT $ 29))
                           (SPADCALL |l| 96 (QREFELT $ 29))
                           (SPADCALL |l| 97 (QREFELT $ 29))
                           (SPADCALL |l| 98 (QREFELT $ 29))
                           (SPADCALL |l| 99 (QREFELT $ 29))))
                    . #1#)
              (LETT |b|
                    (LIST
                     (LIST (SPADCALL |l| 1 (QREFELT $ 29))
                           (SPADCALL |l| 74 (QREFELT $ 29))
                           (SPADCALL |l| 83 (QREFELT $ 29))
                           (SPADCALL |l| 21 (QREFELT $ 29))
                           (SPADCALL |l| 36 (QREFELT $ 29))
                           (SPADCALL |l| 77 (QREFELT $ 29))
                           (SPADCALL |l| 44 (QREFELT $ 29))
                           (SPADCALL |l| 80 (QREFELT $ 29))
                           (SPADCALL |l| 64 (QREFELT $ 29))
                           (SPADCALL |l| 2 (QREFELT $ 29))
                           (SPADCALL |l| 34 (QREFELT $ 29))
                           (SPADCALL |l| 75 (QREFELT $ 29))
                           (SPADCALL |l| 48 (QREFELT $ 29))
                           (SPADCALL |l| 17 (QREFELT $ 29))
                           (SPADCALL |l| 100 (QREFELT $ 29)))
                     (LIST (SPADCALL |l| 3 (QREFELT $ 29))
                           (SPADCALL |l| 15 (QREFELT $ 29))
                           (SPADCALL |l| 31 (QREFELT $ 29))
                           (SPADCALL |l| 52 (QREFELT $ 29))
                           (SPADCALL |l| 19 (QREFELT $ 29))
                           (SPADCALL |l| 11 (QREFELT $ 29))
                           (SPADCALL |l| 73 (QREFELT $ 29))
                           (SPADCALL |l| 79 (QREFELT $ 29))
                           (SPADCALL |l| 26 (QREFELT $ 29))
                           (SPADCALL |l| 56 (QREFELT $ 29))
                           (SPADCALL |l| 41 (QREFELT $ 29))
                           (SPADCALL |l| 99 (QREFELT $ 29))
                           (SPADCALL |l| 39 (QREFELT $ 29))
                           (SPADCALL |l| 84 (QREFELT $ 29))
                           (SPADCALL |l| 90 (QREFELT $ 29)))
                     (LIST (SPADCALL |l| 4 (QREFELT $ 29))
                           (SPADCALL |l| 57 (QREFELT $ 29))
                           (SPADCALL |l| 86 (QREFELT $ 29))
                           (SPADCALL |l| 63 (QREFELT $ 29))
                           (SPADCALL |l| 85 (QREFELT $ 29))
                           (SPADCALL |l| 95 (QREFELT $ 29))
                           (SPADCALL |l| 82 (QREFELT $ 29))
                           (SPADCALL |l| 97 (QREFELT $ 29))
                           (SPADCALL |l| 98 (QREFELT $ 29))
                           (SPADCALL |l| 81 (QREFELT $ 29))
                           (SPADCALL |l| 8 (QREFELT $ 29))
                           (SPADCALL |l| 69 (QREFELT $ 29))
                           (SPADCALL |l| 38 (QREFELT $ 29))
                           (SPADCALL |l| 43 (QREFELT $ 29))
                           (SPADCALL |l| 58 (QREFELT $ 29)))
                     (LIST (SPADCALL |l| 5 (QREFELT $ 29))
                           (SPADCALL |l| 66 (QREFELT $ 29))
                           (SPADCALL |l| 49 (QREFELT $ 29))
                           (SPADCALL |l| 59 (QREFELT $ 29))
                           (SPADCALL |l| 61 (QREFELT $ 29)))
                     (LIST (SPADCALL |l| 6 (QREFELT $ 29))
                           (SPADCALL |l| 68 (QREFELT $ 29))
                           (SPADCALL |l| 89 (QREFELT $ 29))
                           (SPADCALL |l| 94 (QREFELT $ 29))
                           (SPADCALL |l| 92 (QREFELT $ 29))
                           (SPADCALL |l| 20 (QREFELT $ 29))
                           (SPADCALL |l| 13 (QREFELT $ 29))
                           (SPADCALL |l| 54 (QREFELT $ 29))
                           (SPADCALL |l| 24 (QREFELT $ 29))
                           (SPADCALL |l| 51 (QREFELT $ 29))
                           (SPADCALL |l| 87 (QREFELT $ 29))
                           (SPADCALL |l| 27 (QREFELT $ 29))
                           (SPADCALL |l| 76 (QREFELT $ 29))
                           (SPADCALL |l| 23 (QREFELT $ 29))
                           (SPADCALL |l| 67 (QREFELT $ 29)))
                     (LIST (SPADCALL |l| 7 (QREFELT $ 29))
                           (SPADCALL |l| 72 (QREFELT $ 29))
                           (SPADCALL |l| 22 (QREFELT $ 29))
                           (SPADCALL |l| 35 (QREFELT $ 29))
                           (SPADCALL |l| 30 (QREFELT $ 29))
                           (SPADCALL |l| 70 (QREFELT $ 29))
                           (SPADCALL |l| 47 (QREFELT $ 29))
                           (SPADCALL |l| 62 (QREFELT $ 29))
                           (SPADCALL |l| 45 (QREFELT $ 29))
                           (SPADCALL |l| 46 (QREFELT $ 29))
                           (SPADCALL |l| 40 (QREFELT $ 29))
                           (SPADCALL |l| 28 (QREFELT $ 29))
                           (SPADCALL |l| 65 (QREFELT $ 29))
                           (SPADCALL |l| 93 (QREFELT $ 29))
                           (SPADCALL |l| 42 (QREFELT $ 29)))
                     (LIST (SPADCALL |l| 9 (QREFELT $ 29))
                           (SPADCALL |l| 71 (QREFELT $ 29))
                           (SPADCALL |l| 37 (QREFELT $ 29))
                           (SPADCALL |l| 91 (QREFELT $ 29))
                           (SPADCALL |l| 18 (QREFELT $ 29))
                           (SPADCALL |l| 55 (QREFELT $ 29))
                           (SPADCALL |l| 96 (QREFELT $ 29))
                           (SPADCALL |l| 60 (QREFELT $ 29))
                           (SPADCALL |l| 16 (QREFELT $ 29))
                           (SPADCALL |l| 53 (QREFELT $ 29))
                           (SPADCALL |l| 50 (QREFELT $ 29))
                           (SPADCALL |l| 25 (QREFELT $ 29))
                           (SPADCALL |l| 32 (QREFELT $ 29))
                           (SPADCALL |l| 14 (QREFELT $ 29))
                           (SPADCALL |l| 33 (QREFELT $ 29)))
                     (LIST (SPADCALL |l| 10 (QREFELT $ 29))
                           (SPADCALL |l| 78 (QREFELT $ 29))
                           (SPADCALL |l| 88 (QREFELT $ 29))
                           (SPADCALL |l| 29 (QREFELT $ 29))
                           (SPADCALL |l| 12 (QREFELT $ 29))))
                    . #1#)
              (EXIT (|PGE;llli2gp| (LIST |a| |b|) $)))))))))) 

(DEFUN |PGE;janko2;Pg;17| ($) (SPADCALL (|PGE;li1n| 100 $) (QREFELT $ 40))) 

(DEFUN |PGE;abelianGroup;LPg;18| (|l| $)
  (PROG (|element| |gens| #1=#:G1879 |i| #2=#:G1878 #3=#:G1877 |n|)
    (RETURN
     (SEQ (LETT |gens| NIL . #4=(|PGE;abelianGroup;LPg;18|))
          (LETT |element| 1 . #4#)
          (SEQ (LETT |n| NIL . #4#) (LETT #3# |l| . #4#) G190
               (COND
                ((OR (ATOM #3#) (PROGN (LETT |n| (CAR #3#) . #4#) NIL))
                 (GO G191)))
               (SEQ
                (EXIT
                 (COND
                  ((SPADCALL |n| 1 (QREFELT $ 43))
                   (SEQ
                    (LETT |gens|
                          (CONS
                           (SPADCALL
                            (PROGN
                             (LETT #2# NIL . #4#)
                             (SEQ (LETT |i| |element| . #4#)
                                  (LETT #1# (- (+ |element| |n|) 1) . #4#) G190
                                  (COND ((> |i| #1#) (GO G191)))
                                  (SEQ (EXIT (LETT #2# (CONS |i| #2#) . #4#)))
                                  (LETT |i| (+ |i| 1) . #4#) (GO G190) G191
                                  (EXIT (NREVERSE #2#))))
                            (QREFELT $ 21))
                           |gens|)
                          . #4#)
                    (EXIT (LETT |element| (+ |element| |n|) . #4#)))))))
               (LETT #3# (CDR #3#) . #4#) (GO G190) G191 (EXIT NIL))
          (EXIT
           (|PGE;llli2gp|
            (COND ((EQL (LENGTH |gens|) 0) (LIST (LIST (LIST 1)))) ('T |gens|))
            $)))))) 

(DEFUN |PGE;alternatingGroup;LPg;19| (|l| $)
  (PROG (|gens| |tmp| #1=#:G1888 |i| #2=#:G1887)
    (RETURN
     (SEQ
      (LETT |l| (SPADCALL |l| (QREFELT $ 27))
            . #3=(|PGE;alternatingGroup;LPg;19|))
      (EXIT
       (COND
        ((EQL (LENGTH |l|) 0)
         (|error| "Cannot construct alternating group on empty set"))
        ((< (LENGTH |l|) 3)
         (|PGE;llli2gp| (LIST (LIST (LIST (SPADCALL |l| 1 (QREFELT $ 29)))))
          $))
        ((EQL (LENGTH |l|) 3)
         (|PGE;llli2gp|
          (LIST
           (LIST
            (LIST (SPADCALL |l| 1 (QREFELT $ 29))
                  (SPADCALL |l| 2 (QREFELT $ 29))
                  (SPADCALL |l| 3 (QREFELT $ 29)))))
          $))
        (#4='T
         (SEQ
          (LETT |tmp|
                (PROGN
                 (LETT #2# NIL . #3#)
                 (SEQ (LETT |i| 3 . #3#) (LETT #1# (LENGTH |l|) . #3#) G190
                      (COND ((> |i| #1#) (GO G191)))
                      (SEQ
                       (EXIT
                        (LETT #2# (CONS (SPADCALL |l| |i| (QREFELT $ 29)) #2#)
                              . #3#)))
                      (LETT |i| (+ |i| 1) . #3#) (GO G190) G191
                      (EXIT (NREVERSE #2#))))
                . #3#)
          (LETT |gens|
                (LIST (LIST |tmp|)
                      (LIST
                       (LIST (SPADCALL |l| 1 (QREFELT $ 29))
                             (SPADCALL |l| 2 (QREFELT $ 29))
                             (SPADCALL |l| 3 (QREFELT $ 29)))))
                . #3#)
          (EXIT
           (COND ((ODDP (LENGTH |l|)) (|PGE;llli2gp| |gens| $))
                 (#4#
                  (SEQ
                   (SPADCALL |gens| 1
                             (CONS
                              (LIST (SPADCALL |l| 1 (QREFELT $ 29))
                                    (SPADCALL |l| 2 (QREFELT $ 29)))
                              (SPADCALL |gens| 1 (QREFELT $ 46)))
                             (QREFELT $ 47))
                   (EXIT (|PGE;llli2gp| |gens| $)))))))))))))) 

(DEFUN |PGE;alternatingGroup;PiPg;20| (|n| $)
  (SPADCALL (|PGE;li1n| |n| $) (QREFELT $ 48))) 

(DEFUN |PGE;symmetricGroup;LPg;21| (|l| $)
  (SEQ (LETT |l| (SPADCALL |l| (QREFELT $ 27)) |PGE;symmetricGroup;LPg;21|)
       (EXIT
        (COND
         ((EQL (LENGTH |l|) 0)
          (|error| "Cannot construct symmetric group on empty set !"))
         ((< (LENGTH |l|) 3) (|PGE;llli2gp| (LIST (LIST |l|)) $))
         ('T
          (|PGE;llli2gp|
           (LIST (LIST |l|)
                 (LIST
                  (LIST (SPADCALL |l| 1 (QREFELT $ 29))
                        (SPADCALL |l| 2 (QREFELT $ 29)))))
           $)))))) 

(DEFUN |PGE;symmetricGroup;PiPg;22| (|n| $)
  (SPADCALL (|PGE;li1n| |n| $) (QREFELT $ 50))) 

(DEFUN |PGE;cyclicGroup;LPg;23| (|l| $)
  (SEQ (LETT |l| (SPADCALL |l| (QREFELT $ 27)) |PGE;cyclicGroup;LPg;23|)
       (EXIT
        (COND
         ((EQL (LENGTH |l|) 0)
          (|error| "Cannot construct cyclic group on empty set"))
         ('T (|PGE;llli2gp| (LIST (LIST |l|)) $)))))) 

(DEFUN |PGE;cyclicGroup;PiPg;24| (|n| $)
  (SPADCALL (|PGE;li1n| |n| $) (QREFELT $ 52))) 

(DEFUN |PGE;dihedralGroup;LPg;25| (|l| $)
  (PROG (|tmp| #1=#:G1902 |i| #2=#:G1901)
    (RETURN
     (SEQ
      (LETT |l| (SPADCALL |l| (QREFELT $ 27))
            . #3=(|PGE;dihedralGroup;LPg;25|))
      (EXIT
       (COND
        ((< (LENGTH |l|) 3)
         (|error| "in dihedralGroup: Minimum of 3 elements needed !"))
        ('T
         (SEQ
          (LETT |tmp|
                (PROGN
                 (LETT #2# NIL . #3#)
                 (SEQ (LETT |i| 1 . #3#)
                      (LETT #1# (QUOTIENT2 (LENGTH |l|) 2) . #3#) G190
                      (COND ((QSGREATERP |i| #1#) (GO G191)))
                      (SEQ
                       (EXIT
                        (LETT #2#
                              (CONS
                               (LIST (SPADCALL |l| |i| (QREFELT $ 29))
                                     (SPADCALL |l| (+ (- (LENGTH |l|) |i|) 1)
                                               (QREFELT $ 29)))
                               #2#)
                              . #3#)))
                      (LETT |i| (QSADD1 |i|) . #3#) (GO G190) G191
                      (EXIT (NREVERSE #2#))))
                . #3#)
          (EXIT (|PGE;llli2gp| (LIST (LIST |l|) |tmp|) $)))))))))) 

(DEFUN |PGE;dihedralGroup;PiPg;26| (|n| $)
  (COND ((EQL |n| 1) (SPADCALL 2 (QREFELT $ 51)))
        ((EQL |n| 2)
         (|PGE;llli2gp| (LIST (LIST (LIST 1 2)) (LIST (LIST 3 4))) $))
        ('T (SPADCALL (|PGE;li1n| |n| $) (QREFELT $ 54))))) 

(DEFUN |PermutationGroupExamples| #1=()
  (PROG #1#
    (RETURN
     (PROG (#2=#:G1905)
       (RETURN
        (COND
         ((LETT #2# (HGET |$ConstructorCache| '|PermutationGroupExamples|)
                . #3=(|PermutationGroupExamples|))
          (|CDRwithIncrement| (CDAR #2#)))
         ('T
          (UNWIND-PROTECT
              (PROG1
                  (CDDAR
                   (HPUT |$ConstructorCache| '|PermutationGroupExamples|
                         (LIST
                          (CONS NIL (CONS 1 (|PermutationGroupExamples;|))))))
                (LETT #2# T . #3#))
            (COND
             ((NOT #2#)
              (HREM |$ConstructorCache| '|PermutationGroupExamples|))))))))))) 

(DEFUN |PermutationGroupExamples;| ()
  (PROG (|dv$| $ |pv$|)
    (RETURN
     (PROGN
      (LETT |dv$| '(|PermutationGroupExamples|)
            . #1=(|PermutationGroupExamples|))
      (LETT $ (GETREFV 56) . #1#)
      (QSETREFV $ 0 |dv$|)
      (QSETREFV $ 3 (LETT |pv$| (|buildPredVector| 0 0 NIL) . #1#))
      (|haddProp| |$ConstructorCache| '|PermutationGroupExamples| NIL
                  (CONS 1 $))
      (|stuffDomainSlots| $)
      (SETF |pv$| (QREFELT $ 3))
      $)))) 

(MAKEPROP '|PermutationGroupExamples| '|infovec|
          (LIST
           '#(NIL NIL NIL NIL NIL NIL (|List| 20) (|Permutation| 18)
              (0 . |cycles|) (|List| 7) (|Mapping| 7 6) (|List| 6)
              (|ListFunctions2| 6 7) (5 . |map|) (|PermutationGroup| 18)
              (11 . |coerce|) (16 . |One|) (|Boolean|) (|Integer|) (20 . >)
              (|List| 18) (26 . |list|) |PGE;youngGroup;LPg;3| (|Partition|)
              (31 . |convert|) |PGE;youngGroup;PPg;4| |PGE;rubiksGroup;Pg;5|
              (36 . |removeDuplicates|) (41 . ~=) (47 . |elt|)
              |PGE;mathieu11;LPg;6| |PGE;mathieu11;Pg;7| |PGE;mathieu12;LPg;8|
              |PGE;mathieu12;Pg;9| |PGE;mathieu22;LPg;10| |PGE;mathieu22;Pg;11|
              |PGE;mathieu23;LPg;12| |PGE;mathieu23;Pg;13|
              |PGE;mathieu24;LPg;14| |PGE;mathieu24;Pg;15| |PGE;janko2;LPg;16|
              |PGE;janko2;Pg;17| (|PositiveInteger|) (53 . >) (|List| 42)
              |PGE;abelianGroup;LPg;18| (59 . |elt|) (65 . |setelt|)
              |PGE;alternatingGroup;LPg;19| |PGE;alternatingGroup;PiPg;20|
              |PGE;symmetricGroup;LPg;21| |PGE;symmetricGroup;PiPg;22|
              |PGE;cyclicGroup;LPg;23| |PGE;cyclicGroup;PiPg;24|
              |PGE;dihedralGroup;LPg;25| |PGE;dihedralGroup;PiPg;26|)
           '#(|youngGroup| 72 |symmetricGroup| 82 |rubiksGroup| 92 |mathieu24|
              96 |mathieu23| 105 |mathieu22| 114 |mathieu12| 123 |mathieu11|
              132 |janko2| 141 |dihedralGroup| 150 |cyclicGroup| 160
              |alternatingGroup| 170 |abelianGroup| 180)
           'NIL
           (CONS (|makeByteWordVec2| 1 'NIL)
                 (CONS '#()
                       (CONS '#()
                             (|makeByteWordVec2| 55
                                                 '(1 7 0 6 8 2 12 9 10 11 13 1
                                                   14 0 9 15 0 7 0 16 2 18 17 0
                                                   0 19 1 6 0 20 21 1 23 20 0
                                                   24 1 20 0 0 27 2 18 17 0 0
                                                   28 2 20 18 0 18 29 2 42 17 0
                                                   0 43 2 11 6 0 18 46 3 11 6 0
                                                   18 6 47 1 0 14 23 25 1 0 14
                                                   20 22 1 0 14 42 51 1 0 14 20
                                                   50 0 0 14 26 1 0 14 20 38 0
                                                   0 14 39 1 0 14 20 36 0 0 14
                                                   37 0 0 14 35 1 0 14 20 34 1
                                                   0 14 20 32 0 0 14 33 1 0 14
                                                   20 30 0 0 14 31 0 0 14 41 1
                                                   0 14 20 40 1 0 14 20 54 1 0
                                                   14 42 55 1 0 14 42 53 1 0 14
                                                   20 52 1 0 14 42 49 1 0 14 20
                                                   48 1 0 14 44 45)))))
           '|lookupComplete|)) 

(MAKEPROP '|PermutationGroupExamples| 'NILADIC T) 
